It could be tempting a priori to answer `no' to both questions. Indeed first it is recognized for a long time that, in the theory of quantum fields, Bosons are created and annihilated by commutative operators, whereas to Fermions correspond anticommuting operators, so that it is not straightforward to figure out how these two families of operators could be exchanged. Second a `no go' theorem of S. Coleman and J. Mandula [1]} answers negatively to the second question. Note also that a connection between the two questions can be expected, since Bosons and Fermions can also be distinguished by the fact that their fields are transformed in two different ways by the action of the Lorentz group.
